Possible structures for stable carbon clusters of approximately 30100 atoms are considered. On the basis of general chemical arguments, we establish several criteria for stable clusters which implicate hollow, three-dimensional cages with five-and six-membered rings. Approximate energy estimates indicate that cages should be the preferred cluster structure in this size regime. The effects of strain in the -bond system are argued to take a minimum value largely independent of cage size if the curvature of the cage is spread out isotropically. The relative stability of various cages thus depends dominantly on -resonance energies which are computed by several semiempirical methods for a range of cages. All cages of up to 84 sites satisfying our major criteria are identified. All possible icosahedral-symmetry cages (which most strongly satisfy our criteria) are identified, with explicit consideration being given to those with up to 240 sites. In all we make explicit calculations on over 50 cages to check the efficacy of our criteria. Several theoretical conclusions are found to correlate with various molecular beam experiments, and a number of new candidates for especially stable structures are identified. 1988, American Chemical Society. All rights reserved.
